It has different timings but there is a daily, direct flight on Malaysia Airlines between SIN-KCH.
In fact after KCH the aircraft continues onesrds to MYY before coming back.

If you want a confirm border crossing time at Woodlands and you are on foot, you can always try booking a train ticket. Specific schedule with specific passenger limit (may not get a seat though). Clear both immigration formalities before boarding the train in Woodlands CIQ.